The general method for finding the greatest common factor is the same as for finding the greatest common factor of two numbers, using Euclid's method of rolling over and dividing.

Divide polynomials by making vertical equations.

The problem can be done like this: f(x)=x^3(x-1)+(x+1)(x-1)=(x^3+x+1)(x-1)

g(x)=x^2(x-1)+2(x-1)=(x^2+2)(x-1)

∴(f(x),g(x))=x-1